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4 years ago

10

a probability experiment consists of rolling a 6-sided die. find the probability of the event below. rolling a number less than

5

1 answer:

jeka57 [31]4 years ago

6 0

The probability of rolling a number less than 5 on a 6 sided die is 4/6 or 2/3 or 67%

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Find the area that the curve encloses and then sketch it.<br> r = 3 + 8 sin(6)

Rudiy27

Answer:

$A=41\pi\: \text{units}^2\approxA\approx128.8053\:\text{units}^2$

Step-by-step explanation:

I assume you mean $r=3+8\sin\theta$ :

Use the formula $\displaystyle A=\int\limits^a_b \frac{1}{2} {r(\theta)^2} \, d\theta$ where $a$ and $b$ are the lower and upper bounds and $r(\theta)$ is the equation of the polar curve.

Since the graph is symmetrical about the line $\displaystyle \theta=\frac{\pi}{2}$ , let the bounds of integration be $\displaystyle \biggr(-\frac{\pi}{2},\frac{\pi}{2}\biggr)$ to find half the area of the curve, and then find twice of that area:

$\displaystyle A=\int\limits^a_b \frac{1}{2} {r(\theta)^2} \, d\theta\\\\A=2\int\limits^{\frac{\pi}{2}}_{-\frac{\pi}{2}} \frac{1}{2} {(3+8\sin\theta)^2} \, d\theta\\\\A=\int\limits^{\frac{\pi}{2}}_{-\frac{\pi}{2}} 9+48\sin\theta+64\sin^2\theta \, d\theta\\\\A=\int\limits^{\frac{\pi}{2}}_{-\frac{\pi}{2}} 9+48\sin\theta+64\biggr(\frac{1-\cos2\theta}{2} \biggr) \, d\theta\\\\\\A=\int\limits^{\frac{\pi}{2}}_{-\frac{\pi}{2}} (9+48\sin\theta+32-32\cos2\theta) \, d\theta$

$\displaystyle A=\int\limits^{\frac{\pi}{2}}_{-\frac{\pi}{2}} (41+48\sin\theta-32\cos2\theta) \, d\theta\\\\A=41\theta-48\cos\theta-16\sin2\theta\biggr|^{\frac{\pi}{2}}_{-\frac{\pi}{2}}\\\\$

$A=\biggr[41\biggr(\frac{\pi}{2}\biggr)-48\cos\biggr(\frac{\pi}{2}\biggr)-16\sin2\biggr(\frac{\pi}{2}\biggr)\biggr]-\biggr[41\biggr(-\frac{\pi}{2}\biggr)-48\cos\biggr(-\frac{\pi}{2}\biggr)-16\sin2\biggr(-\frac{\pi}{2}\biggr)\biggr]\\\\A=\biggr[\frac{41\pi}{2}-24\sqrt{2}\biggr]-\biggr[-\frac{41\pi}{2}+24\sqrt{2}\biggr]\\ \\A=41\pi\\\\A\approx128.8053$

Thus, the area of the curve is 41π square units. See below for a graph of the curve and its shaded area.

7 0

3 years ago

Amy is 9 years older than her younger sister. if her younger sister is now 1 year old, how many years later will Amy be 4 times

Sholpan [36]

<h3><u>A</u><u>n</u><u>s</u><u>w</u><u>e</u><u>r</u><u>:</u><u>-</u></h3>

Age of Amy's younger sister=1year

☆Amy is 9 years older than her younger sister.

$\\ \sf\longmapsto Age\:of\:Amy=1+9=10years$

Let after x years Amy will be 4times old as her sister.

ATQ

$\\ \sf\longmapsto \dfrac{1+x}{9+x}=\dfrac{1}{4}$

Using cross multiplication

$\\ \sf\longmapsto 4(1+x)=1(9+x)$

$\\ \sf\longmapsto 4+4x=9+x$

$\\ \sf\longmapsto 4x-x=9-4$

$\\ \sf\longmapsto 3x=5$

$\\ \sf\longmapsto x=\dfrac{5}{3}$

$\\ \sf\longmapsto x=1.6$

$\\ \sf\longmapsto x=2(approx)$

5 0

3 years ago

PLS HELP FAST AS U CAN

faltersainse [42]

Answer:

(0,1508)

Step-by-step explanation:

If X is years, and (x,y) is the format, and no years have passed for the first census, then 0 fills in for X and the number of people fills in for y.

5 0

4 years ago

50 Points I need help with this slope I don't understand it, please and thank you!

Len [333]

Answer:

the slope it 3 (:

Step-by-step explanation:

for one on the x axis it goes up three on the y axis

4 0

3 years ago

Find what a equals in this equation.<br><br> <img src="https://tex.z-dn.net/?f=x%28x%2Ba%29%28x%2B3%29%20%3D%20x%28x%2B3%29%28x-

galina1969 [7]

Answer:

a = - 3

Step-by-step explanation:

The equation has common factors x(x + 3) on both sides

For the 2 sides of the equation to be equal, then the factor

(x + a) = (x - 3) and by comparison

a = - 3

4 0

3 years ago